Landau, Zeph ; Sunder, V. S.
(2002)
*Planar depth and planar subalgebras*
Journal of Functional Analysis, 195
(1).
pp. 71-88.
ISSN 0022-1236

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Official URL: http://www.sciencedirect.com/science/article/pii/S...

Related URL: http://dx.doi.org/10.1006/jfan.2002.3937

## Abstract

We consider the notion of planar depth of a planar algebra, viz., the smallest n for which the planar algebra is generated by its 'n-boxes'. We establish a simple result which yields a sufficient condition, in terms of the principal graph of the planar algebra, for the planar depth to be bounded by k. This suffices to determine the planar depth of the E_{6}, E _{8} and the 5+√13/2 subfactors. We then consider a planar subalgebra of the 'group planar algebra' which is naturally associated with a group θ of automorphisms of the given group G. We show that this planar algebra corresponds to the 'subgroup-subfactor' associated with the inclusion θ⊂(G⋊θ) (given by the semi-direct product extension). We conclude with a discussion of the planar depth of this planar algebra P^{θ} in some examples.

Item Type: | Article |
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Source: | Copyright of this article belongs to Elsevier Science. |

Keywords: | Operator Algebras; Subfactor; Planar Algebra; Standard Invariant |

ID Code: | 53540 |

Deposited On: | 09 Aug 2011 11:52 |

Last Modified: | 09 Aug 2011 11:52 |

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